Find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.**

**Two-tailed test, α = 0.05**

---

The critical value(s) is/are z = [___]

*(Round to two decimal places as needed. Use a comma to separate answers as needed.)*

---

**Explanation:**

For a two-tailed test with a significance level of α = 0.05, you will find the critical values by determining the z-scores that correspond to the upper and lower tails of the standard normal distribution that contain 2.5% of the data on each side (because 0.05 divided by two equals 0.025).

Typically, this results in critical z-scores of approximately ±1.96. 

**Graph Explanation:**

The graph for this problem would depict a standard normal distribution curve (bell-shaped) where the rejection regions are shaded at both tails. Each rejection region would contain 2.5% of the data, and the area in the middle (non-rejected region) would contain 95% of the data under the curve. The critical values (z-scores) of approximately ±1.96 mark the boundaries between the rejection and non-rejection regions.
Transcribed Image Text:**Find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.** **Two-tailed test, α = 0.05** --- The critical value(s) is/are z = [___] *(Round to two decimal places as needed. Use a comma to separate answers as needed.)* --- **Explanation:** For a two-tailed test with a significance level of α = 0.05, you will find the critical values by determining the z-scores that correspond to the upper and lower tails of the standard normal distribution that contain 2.5% of the data on each side (because 0.05 divided by two equals 0.025). Typically, this results in critical z-scores of approximately ±1.96. **Graph Explanation:** The graph for this problem would depict a standard normal distribution curve (bell-shaped) where the rejection regions are shaded at both tails. Each rejection region would contain 2.5% of the data, and the area in the middle (non-rejected region) would contain 95% of the data under the curve. The critical values (z-scores) of approximately ±1.96 mark the boundaries between the rejection and non-rejection regions.
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